How to represent the space for the circle

[Fangwq]

I am confused about the space for the circle. In the file circle.py, the notes, in the function _addition_theorem, say that the input param X and X2 are one-dimensional. However, we should represent the circle with two parameters. So, the input should be two-dimensional. How to understand this case? Or, we just denote the space for the circle with the following codes:

ProductDiscreteSpectrumSpace(Circle(), Circle(), num_eigen=num)

Check this code https://github.com/Fangwq/Research-Progress/blob/main/20221201/circle_kernel.py. Are these codes right or not? Thank you very much !

[vabor112]

Hello @Fangwq. The elements of Circle are supposed to be parameterized by their angle. X should consist of angles X[i] from $0$ to $2 \pi$ that correspond to the $(\cos(X[i]), \sin(X[i]))$ point on the circle $\{ \mathbf{v} \in \mathbb{R}^2 : |\mathbf{v}| = 1 \}$.

[vabor112]

Please tell me if this helps.

[Fangwq]

Thank you for your clarification. It works. The codes I have written are wrong.